I didn't find any questions about this, except for this one, but it's not really the same thing.
I've seen the phrase 「知るか」 a few times in anime and manga before and I've always interpreted it as "as if I'd know!".
Recently I came across the phrase 「口が裂けても言うものか」. It confused me a bit because of the conditional that didn't seem to work in a word-for-word translation, but when I searched it on Google, 「口が裂けても言わない」 showed up as a set phrase that means essentially "to keep quiet (about something) no matter what".
So I would translate 「口が裂けても言うものか」 to "as if I'd say that/as if that's something I'd say!". Is that correct?
Finally, I was wondering: is 「知るか」 basically 「知らない」, and 「口が裂けても言うものか」 basically 「口が裂けても言わないもの」, but rude/accusatory? Is it the same for similar exclamatory phrases?
For example, would 「楽しいことか！」, in contrast to 「なんと楽しいことか！」, mean "this isn't fun!"?